Let f:
Question:

Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=\max \left\{x, x^{2}\right\}$. Let $\mathrm{S}$ denote the set of all points in $\mathrm{R}$, where $f$ is not differentiable. Then:

1. (1) $\{0,1\}$

2. (2) $\{0\}$

3. (3) $\phi$ (an empty set)

4. (4) $\{1\}$

Correct Option: 1

Solution:

$f(x)=\max \cdot\left\{x, x^{2}\right\}$

$\Rightarrow f(x)=\left\{\begin{array}{cc}x^{2}, & x<0 \\ x, & 0 \leq x<1 \\ x^{2}, & x \geq 1\end{array}\right.$

$\therefore f(x)$ is not differentiable at $x=0,1$

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